by Ulyanov, Vladimir V., Christoph, Gerd, Fujikoshi, Yasunori.

**Series:** 2006-14, Preprints

- MSC:
- 62H10 Distribution of statistics
- 62E20 Asymptotic distribution theory

**Abstract:**

We get computable error bound of order $O(n^{-1})$ for

chi-squared with 1 degree of freedom approximation of

transformed chi-squared random variable with $n$ degrees of

freedom. The result is applied for likelihood ratio statistics

in multivariate case.

**Keywords:**

Computable error bound, chi-squared approximation, likelihood ratio statistics, transformation of random variables

**This paper was published in:**

Siberian Mathematical Journal, Vol. 47, No. 6, pp. 1154-1166, 2006